{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:XZQ7DWHD52HTJ7WRNV5LHVVAQR","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"bfaac2e91137ac0dee049353c49d27dadd78b81d693e592a42dcdeccf2e79411","cross_cats_sorted":["math.SG"],"license":"","primary_cat":"math.AG","submitted_at":"2004-08-08T11:40:06Z","title_canon_sha256":"ab43f22e121ac17b3076c5d1352dcac9ab5b84fd54466abb4a6e646dc6b6960d"},"schema_version":"1.0","source":{"id":"math/0408101","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0408101","created_at":"2026-05-18T01:38:27Z"},{"alias_kind":"arxiv_version","alias_value":"math/0408101v1","created_at":"2026-05-18T01:38:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0408101","created_at":"2026-05-18T01:38:27Z"},{"alias_kind":"pith_short_12","alias_value":"XZQ7DWHD52HT","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"XZQ7DWHD52HTJ7WR","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"XZQ7DWHD","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:6d0bbcf16038840bf62fc2df5bbe2182baa1598eba7b8c005f2ea5748570138a","target":"graph","created_at":"2026-05-18T01:38:27Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"The complexity of an action of a reductive algebraic group G on an algebraic variety X is the codimension of a generic B-orbit in X, where B is a Borel subgroup of G. We classify affine homogeneous spaces G/H of complexity one. These results are the natural continuation of the classification of spherical affine homogeneous spaces, i.e., spaces of complexity zero.","authors_text":"Ivan V. Arzhantsev, Olga V. Chuvashova","cross_cats":["math.SG"],"headline":"","license":"","primary_cat":"math.AG","submitted_at":"2004-08-08T11:40:06Z","title":"Classification of affine homogeneous spaces of complexity one"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0408101","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:67404bda149f8b5151f2f2c32be94a2e7784829c1117733e39424293ec49949c","target":"record","created_at":"2026-05-18T01:38:27Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"bfaac2e91137ac0dee049353c49d27dadd78b81d693e592a42dcdeccf2e79411","cross_cats_sorted":["math.SG"],"license":"","primary_cat":"math.AG","submitted_at":"2004-08-08T11:40:06Z","title_canon_sha256":"ab43f22e121ac17b3076c5d1352dcac9ab5b84fd54466abb4a6e646dc6b6960d"},"schema_version":"1.0","source":{"id":"math/0408101","kind":"arxiv","version":1}},"canonical_sha256":"be61f1d8e3ee8f34fed16d7ab3d6a0844a41002dd561175d21036459eba1d935","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"be61f1d8e3ee8f34fed16d7ab3d6a0844a41002dd561175d21036459eba1d935","first_computed_at":"2026-05-18T01:38:27.224626Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:38:27.224626Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7Qh3sfr0D8vflnL8xcs9x7832vhxaA+V6Fe3AmTjd5QwS3fPn+mTpXbnDhGJc1lP9wuCsxp1SlLS/xQGybVTCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:38:27.225338Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0408101","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:67404bda149f8b5151f2f2c32be94a2e7784829c1117733e39424293ec49949c","sha256:6d0bbcf16038840bf62fc2df5bbe2182baa1598eba7b8c005f2ea5748570138a"],"state_sha256":"968b7b0a7dfd1093d46697aeab030aaf26a62e23bf5be79176ff288269c9faca"}